Lyapunov spectrum of separated flows and its dependence on numerical discretization

Abstract

We investigate the Lyapunov spectrum of separated flows and their dependence on the numerical discretization. The chaotic flow around the NACA 0012 airfoil at low Reynolds number and large angle of attack is considered to that end, and t-, h- and p-refinement studies are performed to examine each effect separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. In particular, the asymptotic Lyapunov spectrum for time refinement is achieved for CFL numbers as large as $\mathcal{O}(10^1-10^2)$, whereas the system continues to become more and more chaotic even for meshes that are much finer than the best practice for this type of flows.

References in corpus (7)

• Characterizing dynamics with covariant Lyapunov vectors
• Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations
• Lyapunov exponents of heavy particles in turbulence
• Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)
• Recent development of chaos theory in topological dynamics
• Hyperbolic decoupling of tangent space and effective dimension of dissipative systems
• Chaotic Behavior of Stiff ODEs and Their Derivatives: An Illustrative Example

Cited by in corpus (6)

• Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow
• Stability, sensitivity and optimisation of chaotic acoustic oscillations
• Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)
• Feasibility analysis of ensemble sensitivity computation in turbulent flows
• Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)
• Numerical convergence of the Lyapunov spectrum computed using low Mach number solvers